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          <h2 class="post-title" itemprop="name headline">图形化解释PID参数的意义</h2>
        

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        <p>PID算法可以说是应用最广泛的自动控制算法了。以前在学校的时候弄全国大学生电子设计竞赛还有飞思卡尔智能小车的比赛，成天就在摆弄这个东西。但是由于所在专业并没有开自动控制原理的课程，所以其实对于PID的理解是很有限的，只是根据效果机械地调整参数而已。对于参数实际的意义并没有真正理解。<br>参加工作后对更是再也没有接触过了。前几天的时候遇到一个关于动态范围控制的问题，又接触到了反馈控制。于是又把PID算法温习了一遍，这次在具体的模型和Python绘图帮助下，概念清晰了不少。<br><a id="more"></a></p>
<h2 id="水池模型"><a href="#水池模型" class="headerlink" title="水池模型"></a>水池模型</h2><p>为了更好的理解一个抽象概念，最好的办法就是将其具现化。在一个实物模型上将PID用起来。<br>假设这里有个水池，水池有个进水管，有个出水管。</p>
<h2 id="参数P"><a href="#参数P" class="headerlink" title="参数P"></a>参数P</h2><h2 id="参数I"><a href="#参数I" class="headerlink" title="参数I"></a>参数I</h2><h2 id="参数D"><a href="#参数D" class="headerlink" title="参数D"></a>参数D</h2><h2 id="绘图代码"><a href="#绘图代码" class="headerlink" title="绘图代码"></a>绘图代码</h2><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> tkinter <span class="keyword">as</span> tk</span><br><span class="line"><span class="keyword">import</span> math</span><br><span class="line"></span><br><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Application</span><span class="params">(tk.Frame)</span>:</span></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">__init__</span><span class="params">(self, params)</span>:</span></span><br><span class="line">        self.params = params</span><br><span class="line">        self.root = tk.Tk()</span><br><span class="line">        self.root.geometry(<span class="string">"1020x650"</span>)</span><br><span class="line">        self.root.title(<span class="string">'PID'</span>)</span><br><span class="line">        super().__init__(self.root)</span><br><span class="line">        self.pack()</span><br><span class="line">        self.create_widgets()</span><br><span class="line">        self.draw()</span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">create_widgets</span><span class="params">(self)</span>:</span></span><br><span class="line">        self.label = tk.Label(self)</span><br><span class="line">        self.label[<span class="string">"text"</span>] = <span class="string">'PID Demo'</span></span><br><span class="line">        self.label.pack(side = <span class="string">'top'</span>)</span><br><span class="line">        self.cv = tk.Canvas(self,width=<span class="number">1000</span>,height=<span class="number">600</span>,background=<span class="string">"white"</span>)</span><br><span class="line">        self.cv.pack()</span><br><span class="line">    </span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">caculate</span><span class="params">(self,P,I,D,T,L)</span>:</span></span><br><span class="line">        <span class="comment">## P I D Target Length Scale Offset</span></span><br><span class="line">        curve = []</span><br><span class="line">        cur = <span class="number">0</span></span><br><span class="line">        inte = <span class="number">0</span></span><br><span class="line">        err = <span class="number">0</span></span><br><span class="line">        <span class="keyword">for</span> i <span class="keyword">in</span> range(L):</span><br><span class="line">            curve.append(cur)</span><br><span class="line">            diff = T - cur - err</span><br><span class="line">            err = T - cur</span><br><span class="line">            inte += err</span><br><span class="line">            u = P * err + I * inte + D * diff</span><br><span class="line">            cur += u</span><br><span class="line">            <span class="comment">#cur = cur + u - 0.005</span></span><br><span class="line">            <span class="comment">#cur = cur + u - math.sin(i)*0,01</span></span><br><span class="line">        <span class="keyword">return</span> curve</span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">draw</span><span class="params">(self)</span>:</span></span><br><span class="line">        self.cv.create_rectangle(<span class="number">2</span>,<span class="number">2</span>,int(self.cv[<span class="string">"width"</span>]),int(self.cv[<span class="string">"height"</span>]))</span><br><span class="line">        curve = [[]] * len(self.params)</span><br><span class="line">        maxv = <span class="number">0</span></span><br><span class="line">        <span class="keyword">for</span> i <span class="keyword">in</span> range(len(self.params)):</span><br><span class="line">            param = self.params[i]</span><br><span class="line">            curve[i] = self.caculate(param[<span class="number">0</span>], param[<span class="number">1</span>], param[<span class="number">2</span>], param[<span class="number">3</span>],<span class="number">1000</span>)</span><br><span class="line">            <span class="keyword">if</span> max(curve[i]) &gt; maxv:</span><br><span class="line">                maxv = max(curve[i])</span><br><span class="line">        scale = <span class="number">550.0</span> / maxv</span><br><span class="line">        <span class="keyword">if</span> scale &gt; <span class="number">580</span>:</span><br><span class="line">            scale = <span class="number">580</span></span><br><span class="line"></span><br><span class="line">        <span class="keyword">for</span> i <span class="keyword">in</span> range(len(self.params)):</span><br><span class="line">            line = []</span><br><span class="line">            param = self.params[i]</span><br><span class="line">            <span class="keyword">for</span> j <span class="keyword">in</span> range(len(curve[i])):</span><br><span class="line">                line.append(j)</span><br><span class="line">                line.append(<span class="number">600</span> - curve[i][j]*scale)</span><br><span class="line">            self.cv.create_line(line,fill=param[<span class="number">5</span>],width=param[<span class="number">4</span>],smooth=<span class="number">1</span>)</span><br><span class="line"></span><br><span class="line">        self.cv.create_line(<span class="number">0</span>,<span class="number">600</span> - scale,int(self.cv[<span class="string">"width"</span>]),<span class="number">600</span> - scale,width=<span class="number">1</span>,dash=[<span class="number">6</span>,<span class="number">3</span>])</span><br><span class="line">        self.cv.create_line(<span class="number">0</span>,<span class="number">600</span> - <span class="number">0.75</span>*scale,int(self.cv[<span class="string">"width"</span>]),<span class="number">600</span> - <span class="number">0.75</span>*scale,width=<span class="number">1</span>,dash=[<span class="number">4</span>,<span class="number">2</span>],fill=<span class="string">"#aaaaaa"</span>)</span><br><span class="line">        self.cv.create_line(<span class="number">0</span>,<span class="number">600</span> - <span class="number">0.5</span>*scale,int(self.cv[<span class="string">"width"</span>]),<span class="number">600</span> - <span class="number">0.5</span>*scale,width=<span class="number">1</span>,dash=[<span class="number">4</span>,<span class="number">2</span>],fill=<span class="string">"#aaaaaa"</span>)</span><br><span class="line">        self.cv.create_line(<span class="number">0</span>,<span class="number">600</span> - <span class="number">0.25</span>*scale,int(self.cv[<span class="string">"width"</span>]),<span class="number">600</span> - <span class="number">0.25</span>*scale,width=<span class="number">1</span>,dash=[<span class="number">4</span>,<span class="number">2</span>],fill=<span class="string">"#aaaaaa"</span>)</span><br><span class="line"></span><br><span class="line"><span class="comment">#parameters</span></span><br><span class="line"><span class="comment"># P I D Target width color</span></span><br><span class="line">params = [</span><br><span class="line">    [<span class="number">0.05</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">2</span>, <span class="string">"red"</span>],</span><br><span class="line">    [<span class="number">0.03</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">2</span>, <span class="string">"cyan"</span>],</span><br><span class="line">    [<span class="number">0.01</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">2</span>, <span class="string">"purple"</span>]</span><br><span class="line">]</span><br><span class="line"></span><br><span class="line">app = Application(params)</span><br><span class="line">app.mainloop()</span><br></pre></td></tr></table></figure>

      
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